For the complete description of the full base of operators used [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, we refer to [7]}.
To consistently include all terms breaking \(U(3)\) , an \(\mathcal {O}(p^6)\)  odd-intrinsic Lagrangian without resonances must be considered for R\(\chi \) T [3]}.
In addition to the Wess-Zumino-Witten term [2]}, the relevant operators here are
\(\hspace*{85.0pt}\mathcal {O}_7^W&=&i \epsilon _{\mu \nu \alpha \beta } \langle \chi _- f_+^{\mu \nu } f_+^{\alpha \beta }\rangle ,\nonumber \\\mathcal {O}_8^W&=&i \epsilon _{\mu \nu \alpha \beta } \langle \chi _-\rangle \, \langle f_+^{\mu \nu } f_+^{\alpha \beta }\rangle ,\nonumber \\\mathcal {O}_{22}^W&=&i \epsilon _{\mu \nu \alpha \beta } \langle u^\mu \lbrace  \nabla _\rho f_+^{\rho \nu }, f_+^{\alpha \beta }\rbrace \rangle .\) 
